Descartes believed that we should never accept anything about which we can entertain any doubt. So in his attempt to find intellectual certainty, Descartes engaged in a process of methodical doubt, in which he began doubting EVERYTHING until he could find the one thing that could not be doubted. His conclusion was that of all the things that can be doubted, the one thing he couldn't doubt was that he was the one doing the doubting. So Descartes concluded that the one thing he could not doubt was that he existed. He expresses this in the phrase [i:42cac3b3f4]cogito ergo sum[/i:42cac3b3f4], "I think, therefore I am".

But the thing is, it seems to me that Descartes conclusion is a logical fallacy. Isn't he assuming his conclusion ( "I am" ) in his premise ( "I think" )? And if this is really fallacious reasoning, why was Descartes so dumb not to see it?